This study utilizes recently developed threshold cointegration tests that allow for non-linear adjustment between the consumer and producer prices of milk in Greece using data for the period from January 1989 to August 2014. The results reject the null hypothesis of linear cointegration in favor of a two-regime Threshold Autoregressive Model which recognizes the non-stationarity nature of the piece data and allows for an asymmetric price response. In this study the threshold parameter is estimated and implies a minimum decrease (increase) of about 34.12% of the consumer price to place the milk market into regime 1 (regime 2). Note that the corresponding threshold relative markup evaluated at the average farm and retail prices is about 58% where the first regime (1/1989-1/1996) is defined by those values below 58% (with 29% of the observations) while regime 2 (10/1997-8/2014) is defined by values above 58% (with 71% of the observations). The empirical results show that if the equilibrium relative markup is squeezed by more than 58% consumer prices ought to increase faster than producer prices in order to restore long-run equilibrium between consumer-producer milk prices and probably place the milk market into the second regime, since more observations belong in this second regime. The asymmetric price adjustment found in this study, i.e. relative markups higher than 58%, seems to benefit processing companies and retailers and hurt milk producers and consumers. These findings indicate the possible market power of both the milk processing and retail sectors and the limited role of producer organizations. As a result, farmers often see their prices remaining stagnant while consumer prices rise. Farmers consequently receive too little and consumers pay too much. Additionally, the growing concentration of the Greek dairy industry is increasing. The three big dairy processing industries account for 64% of the total market, and along with another three smaller companies account for more than 70% of the milk market.